Average Error: 0.1 → 0.1
Time: 11.2s
Precision: 64
\[x + \frac{x - y}{2}\]
↓
\[1.5 \cdot x - 0.5 \cdot y\]
x + \frac{x - y}{2}
↓
1.5 \cdot x - 0.5 \cdot y
double f(double x, double y) {
        double r338621 = x;
        double r338622 = y;
        double r338623 = r338621 - r338622;
        double r338624 = 2.0;
        double r338625 = r338623 / r338624;
        double r338626 = r338621 + r338625;
        return r338626;
}
↓
double f(double x, double y) {
        double r338627 = 1.5;
        double r338628 = x;
        double r338629 = r338627 * r338628;
        double r338630 = 0.5;
        double r338631 = y;
        double r338632 = r338630 * r338631;
        double r338633 = r338629 - r338632;
        return r338633;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[1.5 \cdot x - 0.5 \cdot y\]

Derivation

  1. Initial program 0.1

    \[x + \frac{x - y}{2}\]

  2. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{1.5 \cdot x - 0.5 \cdot y}\]

  3. Final simplification0.1

    \[\leadsto 1.5 \cdot x - 0.5 \cdot y\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Axis.Types:hBufferRect from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- (* 1.5 x) (* 0.5 y))

  (+ x (/ (- x y) 2)))